TR-2 : Suitability of power transformation based Gumbel EV-1 distribution for flood frequency analysis

Abstract

Estimation of a flood corresponding to a specified recurrence interval at a particular point on a river system is the most common problem for the engineers, scientists and others involved in design and construction of water resources projects. Generally various distributions are fitted with the limited data available at the gauging site of the river system and then a suitable distribution is considered for estimating the floods of required recurrence intervals. Instead of selecting a suitable distribution among the various possible conditions of distributions for fitting the given set of data, it will be more appropriate if the data is transformed to a particular distribution of known characteristics for the purpose of flood frequency analysis. Box-Cox transformation is one of the powerful procedures for transforming the data series to near normalization, which has been employed in flood frequency analysis.

The Gumbel EV-I distribution, is one of the most popular distributions, used for flood frequency analysis and it is more amenable to theoretical analysis. In this study,. an attempt has been made to develop methodology for transforming the annual peak flood series to follow Gumbel EV-I distribution using Box-Cox transformation. The exponent X of the Box-Cox transformation has been estimated by trial and error using the method of maximum likelihood(MML) and method of probability weighted moment(MPWM), so as to obtain nearly the same estimates of log likelihood functions by both the methods. This methodology has been tested using 1000 samples of various sample sizes of randomly generated synthetic "flood" series which follow the Pearsen type HI distribution. The statistical estimates of the reduced variates of the Gumbel EV-I distributed transformed series, viz., mean and standard deviation, have been found nearer to 0.5772 and 1.2825 as required from theoretical considerations and thus verifying the applicability of the proposed methodology for transforming to Gumbel EV-1 distribution. It is seen that the population estimates are satisfactorily reproduced by using the proposed method of frequency analysis.